-LRB- Financial Times -RRB- -- `` It 's very important that Apple not become the developer for the world , '' Tim Cook , Apple chief executive , told analysts last month . `` We need people to invent their own stuff . ''

On Monday , he is due to express those same feelings face-to-face with Choi Gee-Sung , chief executive of Samsung -- the Korean company that Apple alleges is the chief culprit in copying its iPhone and iPad inventions .

Their two days of judge-ordered settlement talks in a San Francisco courthouse will attempt to find a resolution to their rival patent claims , before a full-blown jury trial gets under way , scheduled for July .

This is the key dispute among more than 50 cases that have developed between the two companies over the past year in 10 different countries . Any agreement hammered out here could bring others round the world to a swift conclusion .

`` I do n't know if the parties will settle ; this case is just one part of a very complex ecosystem , and putting CEOs in the room together is always a roll of the dice , '' says Mark Lemley , a professor at Stanford Law School .

`` But both parties need to settle the larger war and get on with innovating . Fighting all the patent battles to the end will leave no one the victor . ''

Apple seems to be the one more eager for a resolution at present , and not just because of Tim Cook 's feelings . `` I 've always hated litigation and I continue to hate it ... I would highly prefer to settle versus battle , '' he said in April .

The urgency for Apple and its lawyers is that Samsung has overtaken it in smartphone sales on the back of Apple 's leadership in innovation . It shipped 45m smartphones in the first quarter , according to Strategy Analytics , compared with Apple 's 35m .

`` Samsung has vaulted into first place in worldwide sales of smartphones , with massive sales of its copycat products , '' alleged a recent Apple filing . `` Samsung 's infringement of Apple 's intellectual property has already resulted in damages that reach billions of dollars . ''

Apple has pursued injunctions and import bans to try to keep not just Samsung out of its markets , but HTC and Motorola as well , all three Samsungbeing users of Google 's rival Android operating system .

HTC 's latest Evo 4G LTE phone was impounded by US Customs last week following an International Trade Commission decision in Apple 's favour . Apple filed on Friday for an injunction to ban Samsung 's Galaxy Tab 10.1 tablet .

The battle with Samsung began in Northern California in April 2011 , with Apple filing a 373-page complaint of patent and trademark infringement . Other skirmishes have since broken out in France , Germany , Italy , Spain , the UK , Netherlands , Australia , Japan and South Korea .

Apple 's original complaint includes allegations that Samsung infringed on elements of the iPhone 's look -- its rectangular shape , rounded corners , silver edges , black face and display of icons . It also alleges Samsung copied features such as the way instant messaging was displayed and even mimicked Apple 's trademarked touch-icons for applications such as Phone , Contacts , Photos and iTunes .

Samsung hit back with its own list of alleged patent infringements by Apple -- backed by its 6,000-strong US telecoms patent portfolio and its claim to have first introduced a smartphone as far back as 1999 . The key patents Samsung relied on all relate to the inner workings of phones and how they connect to 3G networks .

Florian Mueller , an independent patent analyst , says that Samsung could land itself in more trouble by going to war with patents that are essential to standards such as 3G . Antitrust authorities are already investigating whether these should be `` Frand '' patents -- available for anyone to use under `` fair , reasonable and non-discriminatory '' terms .

For its part , Apple is fighting over design elements that are already disappearing in newer models as companies figure out workarounds to possible infringements . For example , Android phones and tablets are `` unlocked '' by swiping from inside a circle on their touchscreens now , rather than swiping along a bar , as on the iPhone .

David Martin , chairman of M-Cam , a US patent analysis company , says there is so much `` prior art '' -- earlier innovations covering similar ground -- that Apple and Samsung are inviting subsequent third-party litigation by airing the strengths and weaknesses of their patents in public .

`` Third-party patent holders , of which there are literally thousands in this space , are salivating over the fact that you are going to have this ongoing acrimony , allowing people essentially to learn where constructive claims of infringement can be made , '' he says .

Apple did not respond to a request for comment on its litigation . Samsung declined to comment .

However , for Apple at least , it is about far more than banning rival products , winning damages or earning royalties in any future licensing agreements , according to Mr Mueller .

`` It 's critical that its products continue to be able to distinguish themselves with unique features , '' he says .

`` That 's what drives consumers to buy them , that 's what sustain its margins and make this all worth tens even hundreds of billions of dollars to Apple . ''

© The Financial Times Limited 2012

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Samsung , Apple begins two days of judge-ordered settlement talks in a San Francisco courthouse

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Attempt to find a resolution to their rival patent claims before a full-blown jury trial gets under way